Energy and area minimizers in metric spaces
- Lytchak, Alexander Mathematisches Institut, Universität Köln, Germany
- Wenger, Stefan Department of Mathematics, University of Fribourg, Switzerland
-
2016
Published in:
- Advances in Calculus of Variations. - 2016, vol. 10, no. 4, p. 407–421
English
We show that in the setting of proper metric spaces one obtains a solution of the classical 2-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area has been chosen appropriately. We prove the quasi- convexity of this new definition of area. Under the assumption of a quadratic isoperimetric inequality we establish regularity results for energy minimizers and improve Hölder exponents of some area-minimizing discs.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
-
- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
-
- RERO DOC 305699
- DOI 10.1515/acv-2015-0027
- Persistent URL
- https://folia.unifr.ch/unifr/documents/306168
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